2 * Minimal code for RSA support from LibTomMath 0.3.9
3 * http://math.libtomcrypt.com/
4 * http://math.libtomcrypt.com/files/ltm-0.39.tar.bz2
5 * This library was released in public domain by Tom St Denis.
7 * The combination in this file is not using many of the optimized algorithms
8 * (e.g., Montgomery reduction) and is considerable slower than the LibTomMath
9 * with its default of SC_RSA_1 settins. The main purpose of having this
10 * version here is to make it easier to build bignum.c wrapper without having
11 * to install and build an external library. However, it is likely worth the
12 * effort to use the full library with SC_RSA_1 instead of this minimized copy.
13 * Including the optimized algorithms may increase the size requirements by
14 * 15 kB or so (measured with x86 build).
16 * If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
17 * libtommath.c file instead of using the external LibTomMath library.
24 #define BN_MP_INVMOD_C
25 #define BN_S_MP_EXPTMOD_C /* Note: #undef in tommath_superclass.h; this would
26 * require BN_MP_EXPTMOD_FAST_C instead */
27 #define BN_S_MP_MUL_DIGS_C
28 #define BN_MP_INVMOD_SLOW_C
30 #define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
31 * would require other than mp_reduce */
37 #define MIN(x,y) ((x)<(y)?(x):(y))
41 #define MAX(x,y) ((x)>(y)?(x):(y))
46 typedef unsigned long mp_digit;
53 #define XMALLOC os_malloc
55 #define XREALLOC os_realloc
58 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
60 #define MP_LT -1 /* less than */
61 #define MP_EQ 0 /* equal to */
62 #define MP_GT 1 /* greater than */
64 #define MP_ZPOS 0 /* positive integer */
65 #define MP_NEG 1 /* negative */
67 #define MP_OKAY 0 /* ok result */
68 #define MP_MEM -2 /* out of mem */
69 #define MP_VAL -3 /* invalid input */
71 #define MP_YES 1 /* yes response */
72 #define MP_NO 0 /* no response */
76 /* define this to use lower memory usage routines (exptmods mostly) */
79 /* default precision */
82 #define MP_PREC 32 /* default digits of precision */
84 #define MP_PREC 8 /* default digits of precision */
88 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
89 #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
91 /* the infamous mp_int structure */
93 int used, alloc, sign;
98 /* ---> Basic Manipulations <--- */
99 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
100 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
101 #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
104 /* prototypes for copied functions */
105 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
106 static int s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
107 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
108 static int s_mp_sqr(mp_int * a, mp_int * b);
109 static int s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
111 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
113 static int mp_init_multi(mp_int *mp, ...);
114 static void mp_clear_multi(mp_int *mp, ...);
115 static int mp_lshd(mp_int * a, int b);
116 static void mp_set(mp_int * a, mp_digit b);
117 static void mp_clamp(mp_int * a);
118 static void mp_exch(mp_int * a, mp_int * b);
119 static void mp_rshd(mp_int * a, int b);
120 static void mp_zero(mp_int * a);
121 static int mp_mod_2d(mp_int * a, int b, mp_int * c);
122 static int mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
123 static int mp_init_copy(mp_int * a, mp_int * b);
124 static int mp_mul_2d(mp_int * a, int b, mp_int * c);
125 static int mp_div_2(mp_int * a, mp_int * b);
126 static int mp_copy(mp_int * a, mp_int * b);
127 static int mp_count_bits(mp_int * a);
128 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
129 static int mp_mod(mp_int * a, mp_int * b, mp_int * c);
130 static int mp_grow(mp_int * a, int size);
131 static int mp_cmp_mag(mp_int * a, mp_int * b);
132 static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
133 static int mp_abs(mp_int * a, mp_int * b);
134 static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
135 static int mp_sqr(mp_int * a, mp_int * b);
136 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
137 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
138 static int mp_2expt(mp_int * a, int b);
139 static int mp_reduce_setup(mp_int * a, mp_int * b);
140 static int mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
141 static int mp_init_size(mp_int * a, int size);
145 /* functions from bn_<func name>.c */
148 /* reverse an array, used for radix code */
149 static void bn_reverse (unsigned char *s, int len)
166 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
167 static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
170 int olduse, res, min, max;
172 /* find sizes, we let |a| <= |b| which means we have to sort
173 * them. "x" will point to the input with the most digits
175 if (a->used > b->used) {
186 if (c->alloc < max + 1) {
187 if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
192 /* get old used digit count and set new one */
197 register mp_digit u, *tmpa, *tmpb, *tmpc;
200 /* alias for digit pointers */
213 for (i = 0; i < min; i++) {
214 /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
215 *tmpc = *tmpa++ + *tmpb++ + u;
217 /* U = carry bit of T[i] */
218 u = *tmpc >> ((mp_digit)DIGIT_BIT);
220 /* take away carry bit from T[i] */
224 /* now copy higher words if any, that is in A+B
225 * if A or B has more digits add those in
228 for (; i < max; i++) {
229 /* T[i] = X[i] + U */
230 *tmpc = x->dp[i] + u;
232 /* U = carry bit of T[i] */
233 u = *tmpc >> ((mp_digit)DIGIT_BIT);
235 /* take away carry bit from T[i] */
243 /* clear digits above oldused */
244 for (i = c->used; i < olduse; i++) {
254 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
255 static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
257 int olduse, res, min, max;
264 if (c->alloc < max) {
265 if ((res = mp_grow (c, max)) != MP_OKAY) {
273 register mp_digit u, *tmpa, *tmpb, *tmpc;
276 /* alias for digit pointers */
281 /* set carry to zero */
283 for (i = 0; i < min; i++) {
284 /* T[i] = A[i] - B[i] - U */
285 *tmpc = *tmpa++ - *tmpb++ - u;
287 /* U = carry bit of T[i]
288 * Note this saves performing an AND operation since
289 * if a carry does occur it will propagate all the way to the
290 * MSB. As a result a single shift is enough to get the carry
292 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
294 /* Clear carry from T[i] */
298 /* now copy higher words if any, e.g. if A has more digits than B */
299 for (; i < max; i++) {
300 /* T[i] = A[i] - U */
303 /* U = carry bit of T[i] */
304 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
306 /* Clear carry from T[i] */
310 /* clear digits above used (since we may not have grown result above) */
311 for (i = c->used; i < olduse; i++) {
321 /* init a new mp_int */
322 static int mp_init (mp_int * a)
326 /* allocate memory required and clear it */
327 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
332 /* set the digits to zero */
333 for (i = 0; i < MP_PREC; i++) {
337 /* set the used to zero, allocated digits to the default precision
338 * and sign to positive */
347 /* clear one (frees) */
348 static void mp_clear (mp_int * a)
352 /* only do anything if a hasn't been freed previously */
354 /* first zero the digits */
355 for (i = 0; i < a->used; i++) {
362 /* reset members to make debugging easier */
364 a->alloc = a->used = 0;
370 /* high level addition (handles signs) */
371 static int mp_add (mp_int * a, mp_int * b, mp_int * c)
375 /* get sign of both inputs */
379 /* handle two cases, not four */
381 /* both positive or both negative */
382 /* add their magnitudes, copy the sign */
384 res = s_mp_add (a, b, c);
386 /* one positive, the other negative */
387 /* subtract the one with the greater magnitude from */
388 /* the one of the lesser magnitude. The result gets */
389 /* the sign of the one with the greater magnitude. */
390 if (mp_cmp_mag (a, b) == MP_LT) {
392 res = s_mp_sub (b, a, c);
395 res = s_mp_sub (a, b, c);
402 /* high level subtraction (handles signs) */
403 static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
411 /* subtract a negative from a positive, OR */
412 /* subtract a positive from a negative. */
413 /* In either case, ADD their magnitudes, */
414 /* and use the sign of the first number. */
416 res = s_mp_add (a, b, c);
418 /* subtract a positive from a positive, OR */
419 /* subtract a negative from a negative. */
420 /* First, take the difference between their */
421 /* magnitudes, then... */
422 if (mp_cmp_mag (a, b) != MP_LT) {
423 /* Copy the sign from the first */
425 /* The first has a larger or equal magnitude */
426 res = s_mp_sub (a, b, c);
428 /* The result has the *opposite* sign from */
429 /* the first number. */
430 c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
431 /* The second has a larger magnitude */
432 res = s_mp_sub (b, a, c);
439 /* high level multiplication (handles sign) */
440 static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
443 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
446 #ifdef BN_MP_TOOM_MUL_C
447 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
448 res = mp_toom_mul(a, b, c);
451 #ifdef BN_MP_KARATSUBA_MUL_C
453 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
454 res = mp_karatsuba_mul (a, b, c);
458 /* can we use the fast multiplier?
460 * The fast multiplier can be used if the output will
461 * have less than MP_WARRAY digits and the number of
462 * digits won't affect carry propagation
464 #ifdef BN_FAST_S_MP_MUL_DIGS_C
465 int digs = a->used + b->used + 1;
467 if ((digs < MP_WARRAY) &&
468 MIN(a->used, b->used) <=
469 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
470 res = fast_s_mp_mul_digs (a, b, c, digs);
473 #ifdef BN_S_MP_MUL_DIGS_C
474 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
476 #error mp_mul could fail
481 c->sign = (c->used > 0) ? neg : MP_ZPOS;
486 /* d = a * b (mod c) */
487 static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
492 if ((res = mp_init (&t)) != MP_OKAY) {
496 if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
500 res = mp_mod (&t, c, d);
506 /* c = a mod b, 0 <= c < b */
507 static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
512 if ((res = mp_init (&t)) != MP_OKAY) {
516 if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
521 if (t.sign != b->sign) {
522 res = mp_add (b, &t, c);
533 /* this is a shell function that calls either the normal or Montgomery
534 * exptmod functions. Originally the call to the montgomery code was
535 * embedded in the normal function but that wasted alot of stack space
536 * for nothing (since 99% of the time the Montgomery code would be called)
538 static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
542 /* modulus P must be positive */
543 if (P->sign == MP_NEG) {
547 /* if exponent X is negative we have to recurse */
548 if (X->sign == MP_NEG) {
549 #ifdef BN_MP_INVMOD_C
553 /* first compute 1/G mod P */
554 if ((err = mp_init(&tmpG)) != MP_OKAY) {
557 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
563 if ((err = mp_init(&tmpX)) != MP_OKAY) {
567 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
568 mp_clear_multi(&tmpG, &tmpX, NULL);
572 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
573 err = mp_exptmod(&tmpG, &tmpX, P, Y);
574 mp_clear_multi(&tmpG, &tmpX, NULL);
577 #error mp_exptmod would always fail
583 /* modified diminished radix reduction */
584 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
585 if (mp_reduce_is_2k_l(P) == MP_YES) {
586 return s_mp_exptmod(G, X, P, Y, 1);
590 #ifdef BN_MP_DR_IS_MODULUS_C
591 /* is it a DR modulus? */
592 dr = mp_dr_is_modulus(P);
598 #ifdef BN_MP_REDUCE_IS_2K_C
599 /* if not, is it a unrestricted DR modulus? */
601 dr = mp_reduce_is_2k(P) << 1;
605 /* if the modulus is odd or dr != 0 use the montgomery method */
606 #ifdef BN_MP_EXPTMOD_FAST_C
607 if (mp_isodd (P) == 1 || dr != 0) {
608 return mp_exptmod_fast (G, X, P, Y, dr);
611 #ifdef BN_S_MP_EXPTMOD_C
612 /* otherwise use the generic Barrett reduction technique */
613 return s_mp_exptmod (G, X, P, Y, 0);
615 #error mp_exptmod could fail
616 /* no exptmod for evens */
619 #ifdef BN_MP_EXPTMOD_FAST_C
625 /* compare two ints (signed)*/
626 static int mp_cmp (mp_int * a, mp_int * b)
628 /* compare based on sign */
629 if (a->sign != b->sign) {
630 if (a->sign == MP_NEG) {
638 if (a->sign == MP_NEG) {
639 /* if negative compare opposite direction */
640 return mp_cmp_mag(b, a);
642 return mp_cmp_mag(a, b);
647 /* compare a digit */
648 static int mp_cmp_d(mp_int * a, mp_digit b)
650 /* compare based on sign */
651 if (a->sign == MP_NEG) {
655 /* compare based on magnitude */
660 /* compare the only digit of a to b */
663 } else if (a->dp[0] < b) {
671 /* hac 14.61, pp608 */
672 static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
674 /* b cannot be negative */
675 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
679 #ifdef BN_FAST_MP_INVMOD_C
680 /* if the modulus is odd we can use a faster routine instead */
681 if (mp_isodd (b) == 1) {
682 return fast_mp_invmod (a, b, c);
686 #ifdef BN_MP_INVMOD_SLOW_C
687 return mp_invmod_slow(a, b, c);
690 #ifndef BN_FAST_MP_INVMOD_C
691 #ifndef BN_MP_INVMOD_SLOW_C
692 #error mp_invmod would always fail
699 /* get the size for an unsigned equivalent */
700 static int mp_unsigned_bin_size (mp_int * a)
702 int size = mp_count_bits (a);
703 return (size / 8 + ((size & 7) != 0 ? 1 : 0));
707 /* hac 14.61, pp608 */
708 static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
710 mp_int x, y, u, v, A, B, C, D;
713 /* b cannot be negative */
714 if (b->sign == MP_NEG || mp_iszero(b) == 1) {
719 if ((res = mp_init_multi(&x, &y, &u, &v,
720 &A, &B, &C, &D, NULL)) != MP_OKAY) {
725 if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
728 if ((res = mp_copy (b, &y)) != MP_OKAY) {
732 /* 2. [modified] if x,y are both even then return an error! */
733 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
738 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
739 if ((res = mp_copy (&x, &u)) != MP_OKAY) {
742 if ((res = mp_copy (&y, &v)) != MP_OKAY) {
749 /* 4. while u is even do */
750 while (mp_iseven (&u) == 1) {
752 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
755 /* 4.2 if A or B is odd then */
756 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
757 /* A = (A+y)/2, B = (B-x)/2 */
758 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
761 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
765 /* A = A/2, B = B/2 */
766 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
769 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
774 /* 5. while v is even do */
775 while (mp_iseven (&v) == 1) {
777 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
780 /* 5.2 if C or D is odd then */
781 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
782 /* C = (C+y)/2, D = (D-x)/2 */
783 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
786 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
790 /* C = C/2, D = D/2 */
791 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
794 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
799 /* 6. if u >= v then */
800 if (mp_cmp (&u, &v) != MP_LT) {
801 /* u = u - v, A = A - C, B = B - D */
802 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
806 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
810 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
814 /* v - v - u, C = C - A, D = D - B */
815 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
819 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
823 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
828 /* if not zero goto step 4 */
829 if (mp_iszero (&u) == 0)
832 /* now a = C, b = D, gcd == g*v */
834 /* if v != 1 then there is no inverse */
835 if (mp_cmp_d (&v, 1) != MP_EQ) {
841 while (mp_cmp_d(&C, 0) == MP_LT) {
842 if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
848 while (mp_cmp_mag(&C, b) != MP_LT) {
849 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
854 /* C is now the inverse */
857 LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
862 /* compare maginitude of two ints (unsigned) */
863 static int mp_cmp_mag (mp_int * a, mp_int * b)
866 mp_digit *tmpa, *tmpb;
868 /* compare based on # of non-zero digits */
869 if (a->used > b->used) {
873 if (a->used < b->used) {
878 tmpa = a->dp + (a->used - 1);
881 tmpb = b->dp + (a->used - 1);
883 /* compare based on digits */
884 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
897 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
898 static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
902 /* make sure there are at least two digits */
904 if ((res = mp_grow(a, 2)) != MP_OKAY) {
912 /* read the bytes in */
914 if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
922 a->dp[0] = (*b & MP_MASK);
923 a->dp[1] |= ((*b++ >> 7U) & 1);
932 /* store in unsigned [big endian] format */
933 static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
938 if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
943 while (mp_iszero (&t) == 0) {
945 b[x++] = (unsigned char) (t.dp[0] & 255);
947 b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
949 if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
960 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
961 static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
968 /* if the shift count is <= 0 then we do no work */
970 res = mp_copy (a, c);
977 if ((res = mp_init (&t)) != MP_OKAY) {
981 /* get the remainder */
983 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
990 if ((res = mp_copy (a, c)) != MP_OKAY) {
995 /* shift by as many digits in the bit count */
996 if (b >= (int)DIGIT_BIT) {
997 mp_rshd (c, b / DIGIT_BIT);
1000 /* shift any bit count < DIGIT_BIT */
1001 D = (mp_digit) (b % DIGIT_BIT);
1003 register mp_digit *tmpc, mask, shift;
1006 mask = (((mp_digit)1) << D) - 1;
1009 shift = DIGIT_BIT - D;
1012 tmpc = c->dp + (c->used - 1);
1016 for (x = c->used - 1; x >= 0; x--) {
1017 /* get the lower bits of this word in a temp */
1020 /* shift the current word and mix in the carry bits from the previous word */
1021 *tmpc = (*tmpc >> D) | (r << shift);
1024 /* set the carry to the carry bits of the current word found above */
1037 static int mp_init_copy (mp_int * a, mp_int * b)
1041 if ((res = mp_init (a)) != MP_OKAY) {
1044 return mp_copy (b, a);
1049 static void mp_zero (mp_int * a)
1058 for (n = 0; n < a->alloc; n++) {
1065 static int mp_copy (mp_int * a, mp_int * b)
1069 /* if dst == src do nothing */
1075 if (b->alloc < a->used) {
1076 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1081 /* zero b and copy the parameters over */
1083 register mp_digit *tmpa, *tmpb;
1085 /* pointer aliases */
1093 /* copy all the digits */
1094 for (n = 0; n < a->used; n++) {
1098 /* clear high digits */
1099 for (; n < b->used; n++) {
1104 /* copy used count and sign */
1111 /* shift right a certain amount of digits */
1112 static void mp_rshd (mp_int * a, int b)
1116 /* if b <= 0 then ignore it */
1121 /* if b > used then simply zero it and return */
1128 register mp_digit *bottom, *top;
1130 /* shift the digits down */
1135 /* top [offset into digits] */
1138 /* this is implemented as a sliding window where
1139 * the window is b-digits long and digits from
1140 * the top of the window are copied to the bottom
1144 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
1146 \-------------------/ ---->
1148 for (x = 0; x < (a->used - b); x++) {
1152 /* zero the top digits */
1153 for (; x < a->used; x++) {
1158 /* remove excess digits */
1163 /* swap the elements of two integers, for cases where you can't simply swap the
1164 * mp_int pointers around
1166 static void mp_exch (mp_int * a, mp_int * b)
1176 /* trim unused digits
1178 * This is used to ensure that leading zero digits are
1179 * trimed and the leading "used" digit will be non-zero
1180 * Typically very fast. Also fixes the sign if there
1181 * are no more leading digits
1183 static void mp_clamp (mp_int * a)
1185 /* decrease used while the most significant digit is
1188 while (a->used > 0 && a->dp[a->used - 1] == 0) {
1192 /* reset the sign flag if used == 0 */
1199 /* grow as required */
1200 static int mp_grow (mp_int * a, int size)
1205 /* if the alloc size is smaller alloc more ram */
1206 if (a->alloc < size) {
1207 /* ensure there are always at least MP_PREC digits extra on top */
1208 size += (MP_PREC * 2) - (size % MP_PREC);
1210 /* reallocate the array a->dp
1212 * We store the return in a temporary variable
1213 * in case the operation failed we don't want
1214 * to overwrite the dp member of a.
1216 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
1218 /* reallocation failed but "a" is still valid [can be freed] */
1222 /* reallocation succeeded so set a->dp */
1225 /* zero excess digits */
1228 for (; i < a->alloc; i++) {
1238 * Simple function copies the input and fixes the sign to positive
1240 static int mp_abs (mp_int * a, mp_int * b)
1246 if ((res = mp_copy (a, b)) != MP_OKAY) {
1251 /* force the sign of b to positive */
1258 /* set to a digit */
1259 static void mp_set (mp_int * a, mp_digit b)
1262 a->dp[0] = b & MP_MASK;
1263 a->used = (a->dp[0] != 0) ? 1 : 0;
1268 static int mp_div_2(mp_int * a, mp_int * b)
1270 int x, res, oldused;
1273 if (b->alloc < a->used) {
1274 if ((res = mp_grow (b, a->used)) != MP_OKAY) {
1282 register mp_digit r, rr, *tmpa, *tmpb;
1285 tmpa = a->dp + b->used - 1;
1288 tmpb = b->dp + b->used - 1;
1292 for (x = b->used - 1; x >= 0; x--) {
1293 /* get the carry for the next iteration */
1296 /* shift the current digit, add in carry and store */
1297 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
1299 /* forward carry to next iteration */
1303 /* zero excess digits */
1304 tmpb = b->dp + b->used;
1305 for (x = b->used; x < oldused; x++) {
1315 /* shift left by a certain bit count */
1316 static int mp_mul_2d (mp_int * a, int b, mp_int * c)
1323 if ((res = mp_copy (a, c)) != MP_OKAY) {
1328 if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
1329 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
1334 /* shift by as many digits in the bit count */
1335 if (b >= (int)DIGIT_BIT) {
1336 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
1341 /* shift any bit count < DIGIT_BIT */
1342 d = (mp_digit) (b % DIGIT_BIT);
1344 register mp_digit *tmpc, shift, mask, r, rr;
1347 /* bitmask for carries */
1348 mask = (((mp_digit)1) << d) - 1;
1350 /* shift for msbs */
1351 shift = DIGIT_BIT - d;
1358 for (x = 0; x < c->used; x++) {
1359 /* get the higher bits of the current word */
1360 rr = (*tmpc >> shift) & mask;
1362 /* shift the current word and OR in the carry */
1363 *tmpc = ((*tmpc << d) | r) & MP_MASK;
1366 /* set the carry to the carry bits of the current word */
1370 /* set final carry */
1372 c->dp[(c->used)++] = r;
1380 static int mp_init_multi(mp_int *mp, ...)
1382 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
1383 int n = 0; /* Number of ok inits */
1384 mp_int* cur_arg = mp;
1387 va_start(args, mp); /* init args to next argument from caller */
1388 while (cur_arg != NULL) {
1389 if (mp_init(cur_arg) != MP_OKAY) {
1390 /* Oops - error! Back-track and mp_clear what we already
1391 succeeded in init-ing, then return error.
1395 /* end the current list */
1398 /* now start cleaning up */
1400 va_start(clean_args, mp);
1403 cur_arg = va_arg(clean_args, mp_int*);
1410 cur_arg = va_arg(args, mp_int*);
1413 return res; /* Assumed ok, if error flagged above. */
1417 static void mp_clear_multi(mp_int *mp, ...)
1419 mp_int* next_mp = mp;
1422 while (next_mp != NULL) {
1424 next_mp = va_arg(args, mp_int*);
1430 /* shift left a certain amount of digits */
1431 static int mp_lshd (mp_int * a, int b)
1435 /* if its less than zero return */
1440 /* grow to fit the new digits */
1441 if (a->alloc < a->used + b) {
1442 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
1448 register mp_digit *top, *bottom;
1450 /* increment the used by the shift amount then copy upwards */
1454 top = a->dp + a->used - 1;
1457 bottom = a->dp + a->used - 1 - b;
1459 /* much like mp_rshd this is implemented using a sliding window
1460 * except the window goes the otherway around. Copying from
1461 * the bottom to the top. see bn_mp_rshd.c for more info.
1463 for (x = a->used - 1; x >= b; x--) {
1467 /* zero the lower digits */
1469 for (x = 0; x < b; x++) {
1477 /* returns the number of bits in an int */
1478 static int mp_count_bits (mp_int * a)
1488 /* get number of digits and add that */
1489 r = (a->used - 1) * DIGIT_BIT;
1491 /* take the last digit and count the bits in it */
1492 q = a->dp[a->used - 1];
1493 while (q > ((mp_digit) 0)) {
1495 q >>= ((mp_digit) 1);
1501 /* calc a value mod 2**b */
1502 static int mp_mod_2d (mp_int * a, int b, mp_int * c)
1506 /* if b is <= 0 then zero the int */
1512 /* if the modulus is larger than the value than return */
1513 if (b >= (int) (a->used * DIGIT_BIT)) {
1514 res = mp_copy (a, c);
1519 if ((res = mp_copy (a, c)) != MP_OKAY) {
1523 /* zero digits above the last digit of the modulus */
1524 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
1527 /* clear the digit that is not completely outside/inside the modulus */
1528 c->dp[b / DIGIT_BIT] &=
1529 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
1535 /* slower bit-bang division... also smaller */
1536 static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
1538 mp_int ta, tb, tq, q;
1541 /* is divisor zero ? */
1542 if (mp_iszero (b) == 1) {
1546 /* if a < b then q=0, r = a */
1547 if (mp_cmp_mag (a, b) == MP_LT) {
1549 res = mp_copy (a, d);
1559 /* init our temps */
1560 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
1566 n = mp_count_bits(a) - mp_count_bits(b);
1567 if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
1568 ((res = mp_abs(b, &tb)) != MP_OKAY) ||
1569 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
1570 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
1575 if (mp_cmp(&tb, &ta) != MP_GT) {
1576 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
1577 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
1581 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
1582 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
1587 /* now q == quotient and ta == remainder */
1589 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
1592 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
1596 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
1599 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
1607 #define TAB_SIZE 256
1610 static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
1612 mp_int M[TAB_SIZE], res, mu;
1614 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
1615 int (*redux)(mp_int*,mp_int*,mp_int*);
1617 /* find window size */
1618 x = mp_count_bits (X);
1621 } else if (x <= 36) {
1623 } else if (x <= 140) {
1625 } else if (x <= 450) {
1627 } else if (x <= 1303) {
1629 } else if (x <= 3529) {
1642 /* init first cell */
1643 if ((err = mp_init(&M[1])) != MP_OKAY) {
1647 /* now init the second half of the array */
1648 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
1649 if ((err = mp_init(&M[x])) != MP_OKAY) {
1650 for (y = 1<<(winsize-1); y < x; y++) {
1658 /* create mu, used for Barrett reduction */
1659 if ((err = mp_init (&mu)) != MP_OKAY) {
1664 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
1669 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
1672 redux = mp_reduce_2k_l;
1677 * The M table contains powers of the base,
1678 * e.g. M[x] = G**x mod P
1680 * The first half of the table is not
1681 * computed though accept for M[0] and M[1]
1683 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
1687 /* compute the value at M[1<<(winsize-1)] by squaring
1688 * M[1] (winsize-1) times
1690 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
1694 for (x = 0; x < (winsize - 1); x++) {
1696 if ((err = mp_sqr (&M[1 << (winsize - 1)],
1697 &M[1 << (winsize - 1)])) != MP_OKAY) {
1701 /* reduce modulo P */
1702 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
1707 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
1708 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
1710 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
1711 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
1714 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
1720 if ((err = mp_init (&res)) != MP_OKAY) {
1725 /* set initial mode and bit cnt */
1729 digidx = X->used - 1;
1734 /* grab next digit as required */
1735 if (--bitcnt == 0) {
1736 /* if digidx == -1 we are out of digits */
1740 /* read next digit and reset the bitcnt */
1741 buf = X->dp[digidx--];
1742 bitcnt = (int) DIGIT_BIT;
1745 /* grab the next msb from the exponent */
1746 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
1747 buf <<= (mp_digit)1;
1749 /* if the bit is zero and mode == 0 then we ignore it
1750 * These represent the leading zero bits before the first 1 bit
1751 * in the exponent. Technically this opt is not required but it
1752 * does lower the # of trivial squaring/reductions used
1754 if (mode == 0 && y == 0) {
1758 /* if the bit is zero and mode == 1 then we square */
1759 if (mode == 1 && y == 0) {
1760 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
1763 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
1769 /* else we add it to the window */
1770 bitbuf |= (y << (winsize - ++bitcpy));
1773 if (bitcpy == winsize) {
1774 /* ok window is filled so square as required and multiply */
1776 for (x = 0; x < winsize; x++) {
1777 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
1780 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
1786 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
1789 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
1793 /* empty window and reset */
1800 /* if bits remain then square/multiply */
1801 if (mode == 2 && bitcpy > 0) {
1802 /* square then multiply if the bit is set */
1803 for (x = 0; x < bitcpy; x++) {
1804 if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
1807 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
1812 if ((bitbuf & (1 << winsize)) != 0) {
1814 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
1817 if ((err = redux (&res, P, &mu)) != MP_OKAY) {
1826 LBL_RES:mp_clear (&res);
1827 LBL_MU:mp_clear (&mu);
1830 for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
1837 /* computes b = a*a */
1838 static int mp_sqr (mp_int * a, mp_int * b)
1842 #ifdef BN_MP_TOOM_SQR_C
1843 /* use Toom-Cook? */
1844 if (a->used >= TOOM_SQR_CUTOFF) {
1845 res = mp_toom_sqr(a, b);
1849 #ifdef BN_MP_KARATSUBA_SQR_C
1850 if (a->used >= KARATSUBA_SQR_CUTOFF) {
1851 res = mp_karatsuba_sqr (a, b);
1855 #ifdef BN_FAST_S_MP_SQR_C
1856 /* can we use the fast comba multiplier? */
1857 if ((a->used * 2 + 1) < MP_WARRAY &&
1859 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
1860 res = fast_s_mp_sqr (a, b);
1863 #ifdef BN_S_MP_SQR_C
1864 res = s_mp_sqr (a, b);
1866 #error mp_sqr could fail
1875 /* reduces a modulo n where n is of the form 2**p - d
1876 This differs from reduce_2k since "d" can be larger
1877 than a single digit.
1879 static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
1884 if ((res = mp_init(&q)) != MP_OKAY) {
1888 p = mp_count_bits(n);
1890 /* q = a/2**p, a = a mod 2**p */
1891 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
1896 if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
1901 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
1905 if (mp_cmp_mag(a, n) != MP_LT) {
1916 /* determines the setup value */
1917 static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
1922 if ((res = mp_init(&tmp)) != MP_OKAY) {
1926 if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
1930 if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
1940 /* computes a = 2**b
1942 * Simple algorithm which zeroes the int, grows it then just sets one bit
1945 static int mp_2expt (mp_int * a, int b)
1949 /* zero a as per default */
1952 /* grow a to accomodate the single bit */
1953 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
1957 /* set the used count of where the bit will go */
1958 a->used = b / DIGIT_BIT + 1;
1960 /* put the single bit in its place */
1961 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
1967 /* pre-calculate the value required for Barrett reduction
1968 * For a given modulus "b" it calulates the value required in "a"
1970 static int mp_reduce_setup (mp_int * a, mp_int * b)
1974 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
1977 return mp_div (a, b, a, NULL);
1981 /* reduces x mod m, assumes 0 < x < m**2, mu is
1982 * precomputed via mp_reduce_setup.
1983 * From HAC pp.604 Algorithm 14.42
1985 static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
1988 int res, um = m->used;
1991 if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
1995 /* q1 = x / b**(k-1) */
1996 mp_rshd (&q, um - 1);
1998 /* according to HAC this optimization is ok */
1999 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
2000 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
2004 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
2005 if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2008 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
2009 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
2014 #error mp_reduce would always fail
2021 /* q3 = q2 / b**(k+1) */
2022 mp_rshd (&q, um + 1);
2024 /* x = x mod b**(k+1), quick (no division) */
2025 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
2029 /* q = q * m mod b**(k+1), quick (no division) */
2030 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
2035 if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
2039 /* If x < 0, add b**(k+1) to it */
2040 if (mp_cmp_d (x, 0) == MP_LT) {
2042 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
2045 if ((res = mp_add (x, &q, x)) != MP_OKAY) {
2050 /* Back off if it's too big */
2051 while (mp_cmp (x, m) != MP_LT) {
2052 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
2064 /* multiplies |a| * |b| and only computes upto digs digits of result
2065 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
2066 * many digits of output are created.
2068 static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2071 int res, pa, pb, ix, iy;
2074 mp_digit tmpx, *tmpt, *tmpy;
2076 /* can we use the fast multiplier? */
2077 if (((digs) < MP_WARRAY) &&
2078 MIN (a->used, b->used) <
2079 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2080 return fast_s_mp_mul_digs (a, b, c, digs);
2083 if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
2088 /* compute the digits of the product directly */
2090 for (ix = 0; ix < pa; ix++) {
2091 /* set the carry to zero */
2094 /* limit ourselves to making digs digits of output */
2095 pb = MIN (b->used, digs - ix);
2097 /* setup some aliases */
2098 /* copy of the digit from a used within the nested loop */
2101 /* an alias for the destination shifted ix places */
2104 /* an alias for the digits of b */
2107 /* compute the columns of the output and propagate the carry */
2108 for (iy = 0; iy < pb; iy++) {
2109 /* compute the column as a mp_word */
2110 r = ((mp_word)*tmpt) +
2111 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2114 /* the new column is the lower part of the result */
2115 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2117 /* get the carry word from the result */
2118 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
2120 /* set carry if it is placed below digs */
2121 if (ix + iy < digs) {
2134 /* Fast (comba) multiplier
2136 * This is the fast column-array [comba] multiplier. It is
2137 * designed to compute the columns of the product first
2138 * then handle the carries afterwards. This has the effect
2139 * of making the nested loops that compute the columns very
2140 * simple and schedulable on super-scalar processors.
2142 * This has been modified to produce a variable number of
2143 * digits of output so if say only a half-product is required
2144 * you don't have to compute the upper half (a feature
2145 * required for fast Barrett reduction).
2147 * Based on Algorithm 14.12 on pp.595 of HAC.
2150 static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2152 int olduse, res, pa, ix, iz;
2153 mp_digit W[MP_WARRAY];
2154 register mp_word _W;
2156 /* grow the destination as required */
2157 if (c->alloc < digs) {
2158 if ((res = mp_grow (c, digs)) != MP_OKAY) {
2163 /* number of output digits to produce */
2164 pa = MIN(digs, a->used + b->used);
2166 /* clear the carry */
2168 for (ix = 0; ix < pa; ix++) {
2171 mp_digit *tmpx, *tmpy;
2173 /* get offsets into the two bignums */
2174 ty = MIN(b->used-1, ix);
2177 /* setup temp aliases */
2181 /* this is the number of times the loop will iterrate, essentially
2182 while (tx++ < a->used && ty-- >= 0) { ... }
2184 iy = MIN(a->used-tx, ty+1);
2187 for (iz = 0; iz < iy; ++iz) {
2188 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
2193 W[ix] = ((mp_digit)_W) & MP_MASK;
2195 /* make next carry */
2196 _W = _W >> ((mp_word)DIGIT_BIT);
2204 register mp_digit *tmpc;
2206 for (ix = 0; ix < pa+1; ix++) {
2207 /* now extract the previous digit [below the carry] */
2211 /* clear unused digits [that existed in the old copy of c] */
2212 for (; ix < olduse; ix++) {
2221 /* init an mp_init for a given size */
2222 static int mp_init_size (mp_int * a, int size)
2226 /* pad size so there are always extra digits */
2227 size += (MP_PREC * 2) - (size % MP_PREC);
2230 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
2231 if (a->dp == NULL) {
2235 /* set the members */
2240 /* zero the digits */
2241 for (x = 0; x < size; x++) {
2249 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
2250 static int s_mp_sqr (mp_int * a, mp_int * b)
2253 int res, ix, iy, pa;
2255 mp_digit u, tmpx, *tmpt;
2258 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
2262 /* default used is maximum possible size */
2265 for (ix = 0; ix < pa; ix++) {
2266 /* first calculate the digit at 2*ix */
2267 /* calculate double precision result */
2268 r = ((mp_word) t.dp[2*ix]) +
2269 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
2271 /* store lower part in result */
2272 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
2275 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2277 /* left hand side of A[ix] * A[iy] */
2280 /* alias for where to store the results */
2281 tmpt = t.dp + (2*ix + 1);
2283 for (iy = ix + 1; iy < pa; iy++) {
2284 /* first calculate the product */
2285 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
2287 /* now calculate the double precision result, note we use
2288 * addition instead of *2 since it's easier to optimize
2290 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
2292 /* store lower part */
2293 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2296 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2298 /* propagate upwards */
2299 while (u != ((mp_digit) 0)) {
2300 r = ((mp_word) *tmpt) + ((mp_word) u);
2301 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2302 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
2313 /* multiplies |a| * |b| and does not compute the lower digs digits
2314 * [meant to get the higher part of the product]
2316 static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
2319 int res, pa, pb, ix, iy;
2322 mp_digit tmpx, *tmpt, *tmpy;
2324 /* can we use the fast multiplier? */
2325 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
2326 if (((a->used + b->used + 1) < MP_WARRAY)
2327 && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
2328 return fast_s_mp_mul_high_digs (a, b, c, digs);
2332 if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
2335 t.used = a->used + b->used + 1;
2339 for (ix = 0; ix < pa; ix++) {
2340 /* clear the carry */
2343 /* left hand side of A[ix] * B[iy] */
2346 /* alias to the address of where the digits will be stored */
2347 tmpt = &(t.dp[digs]);
2349 /* alias for where to read the right hand side from */
2350 tmpy = b->dp + (digs - ix);
2352 for (iy = digs - ix; iy < pb; iy++) {
2353 /* calculate the double precision result */
2354 r = ((mp_word)*tmpt) +
2355 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
2358 /* get the lower part */
2359 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
2361 /* carry the carry */
2362 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));